Group+5+(1)

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Here are two examples of a function (y) and its first (y') and second (y") derivative:



Listen to the Voki characters below to learn about the graph to the left. media type="custom" key="6302321" media type="custom" key="6302469" ​



Practice drawing the derivative graph [|HERE] Important Vocabulary to Know: ​
 * __Relative/Local Maximums:__ any max value on a given interval and can be the absolute maximum, but can never occur at an endpoint
 * __Relative/Local Minimums:__ any min value on a given interval and can be the absolute minimum, but can never occur at an endpoint
 * __Absolute Maximum:__ the highest point pictured on the graph that can occur on an endpoint
 * __Absolute Minimum:__ the lowest point picture on the graph that can occur on an endpoint
 * __Critical Number:__ a number "c" in the domain of a function such that the derivative at "c" equals zero or the derivative at "c" does not exist.

Listen to another vocab word.media type="file" key="Point of Inflection.mp3" width="240" height="20"

Watch the following videos on maxima and minima, critical points and concavity for extra review.

[|Video 1] [|Video 2] [|Video 3]

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Now listen to a song about maximums and minimums below.

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The Mean Value Theorem The Mean Value Theorem states that if f is a differential function on the interval [a,b], then there exists a number c between a and b such that: f'(c) = f(b) - f(a) / b - a

These two graphs below visually represent the mean value theorem.

See an example using the Mean Value Theorem here:

Works Cited: